
Gaussian case: \(p=2\) , \(f_0(z)={\rm const}\) , \(y^2=z^2-{\rm const}\) . This leads to the notorious semi-circle distribution [1]}, and the Riemann surface has genus 0, it is just sphere.

Cubic polynomial \(W_3\)  case: \(p=3\) , \(f_1(z)\)  is a linear function, the spectral curve is a torus, the space of solutions is described by a function of one variable.

